| 徐兴海,刘宏亮,欧阳自根,肖其珍.具斥力函数的奇异Cucker-Smale模型的渐近免碰撞集群[J].南华大学学报(自然科学版),2022,(6):51~57.[XU Xinghai,LIU Hongliang,OUYANG Zigen,XIAO Qizhen.Asymptotic Collision-avoidance Flocking of Singular Cucker-Smale Models with Repulsion Functions[J].Journal of University of South China(Science and Technology),2022,(6):51~57.] |
| 具斥力函数的奇异Cucker-Smale模型的渐近免碰撞集群 |
| Asymptotic Collision-avoidance Flocking of Singular Cucker-Smale Models with Repulsion Functions |
| 投稿时间：2022-06-30 |
| DOI： |
| 中文关键词: 避免碰撞 能量函数 Cucker-Smale模型 集群 |
| 英文关键词:collision-avoidance energy function Cuker-Samle model flocking |
| 基金项目:湖南省自然科学基金项目(2020JJ6003;2021JJ30567);湖南省教育厅重点项目(20A425) |
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| 中文摘要: |
| 针对一个改进的Cucker-Samle模型的免碰撞问题,利用奇异权函数与排斥力结合的方法,证明了当排斥力函数中的幂指数m∈[1,2)时只要系统中的粒子在初始时刻不发生碰撞,系统的集群会无条件发生且粒子不会发生碰撞.最后数值模拟进一步验证理论结论正确性 |
| 英文摘要: |
| This paper considers, we consider the method of combining singular weight function with repulsive force for an improved Cucker-Samle model’s collision-avoidance problem, and prove that when the power of the repulsive force function m∈[1,2), as long as the particles in the system do not collide at the initial moment, the flocking of the system will occur unconditionally and the particles will not collide. Finally, numerical simulation further verifies the correctness of the theoretical conclusion. |
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